1. Field of the Invention
The present invention relates to a color conversion method and a color conversion table generating apparatus for converting a color signal from a first colorimetric system to a second colorimetric system.
2. Description of the Related Art
For recording color images with an image output apparatus such as a color printer or the like, it is possible to realize color images having desired colors by manipulating color signals of colors C (cyan), M (magenta), Y (yellow). Since the color signals depend upon the output characteristics of the image output apparatus, any color signals supplied from an external apparatus having different characteristics need to be converted by a color conversion process raking the output characteristics into account.
According to one conventional method, a plurality of known color patches in different colors are generated using the image output apparatus. The color patches are colorimetrically analyzed to produce a conversion relationship (hereinafter referred to as a "forward conversion relationship") for converting known color signals CMY of the color patches into stimulus signals XYZ. Then, a conversion relationship (hereinafter referred to as a "reverse conversion relationship") for converting the stimulus signals XYZ back into color signals CMY is determined. The above color conversion process is carried out using the reverse conversion relationship.
FIG. 9 of the accompanying drawings shows a two-dimensional representation of the forward and reverse conversion relationships between known color signals CMY of color patches generated at regular grid intervals and stimulus signals XYZ. The color signals CMY at respective grid points in a CMY colorimetric system correspond to the stimulus signals XYZ at respective grid points in an XYZ colorimetric system. Since grid intervals are highly irregular in the XYZ colorimetric system, when color signals CMY corresponding to stimulus signals XYZ at a point A are to be determined, interpolating calculations tend to be effected using color signals CMY at points A3, A4, A5, A6 near the point A while in fact interpolating calculations should be effected using color signals CMY at points A1, A2, A3, A4. It is therefore highly difficult to determine grid points surrounding any optional stimulus signals XYZ for a reverse conversion process.
There has been known a process of determining color signals CMY from stimulus signals XYZ by setting up a tetrahedron whose vertexes are provided by stimulus signals XYZ of four points, dividing a space of the stimulus signals XYZ with the tetrahedron, similarly dividing a space of color signals CMY with a tetrahedron, and determining color signals CMY with respect to any optional stimulus signals XYZ in the corresponding tetrahedron according to linear calculations (see Japanese laid-open patent publication No. 3-18179). According to another process, color signals CMY corresponding to any optional stimulus signals XYZ are determined according to repetitive calculations using the Newton's method (see PHOTOGRAPHIC SCIENCE AND ENGINEERING, Volume 16, Number 2, March-April 1972, pp. 136-143 "Metameric color matching in subtractive color photography").
According to the former process, however, as the space of the stimulus signals XYZ is more and more distorted, the risk of an inappropriate choice of the stimulus signals XYZ of four points making up the tetrahedron becomes larger, making it more difficult to search for corresponding color signals CMY with precision.
According to the latter process, since the forward conversion relationship obtained from the color patches has a limited range, there may possibly be occasions where it is impossible to continue the repetitive calculations while in progress. One solution would be to insert a damping coefficient to keep calculated values produced by the repetitive calculations within the limited range. However, the damping coefficient would have to be established on a trial-and-error basis, and the calculations may possibly fail to converge in the vicinity of the boundaries of the range. Establishing hypothetical stimulus signals XYZ and color signals CMY outside the range may make it possible to sustain the calculations, but accurate color signals CMY may not be obtained depending on the manner in which those hypothetical stimulus signals XYZ and color signals CMY are established.